how many kgs of rice costing rs 12 a kg be mixed with 22kgs of rice costing rs 18 a kg to get a mixture costing rs 16.40 a kg?
Answers
Answer:
The required quantity is 8 kg
Step-by-step explanation:
Part 1
Let "x" be the quantity of rice in kg, costing Rs.12 per kg
Value of this rice = 12x
22 kg of rice costing Rs.18 will have value 22*18 = Rs.396
The total value of the mixture = 12x + 396 ........(i)
Part 2
The mixture will weigh (22 + x) kg and will cost Rs.16.40 per kg
=> The value of the mixture = 16.4*(22 + x)
= 360.8 + 16.4x ......(ii)
Thus, we have got the value of the mixture in two ways. Clearly, (i) = (ii)
=> 12x + 396 = 306.8 + 16.4x
=> 16.4x - 12x = 396 - 306.8
=> 4.4x = 35.2
=> x = 35.2/4.4
=> x = 8
The required quantity of rice is 8 kg
Verification:
8 kg of rice, costing Rs.12 per kg, will have value Rs.96
22 kg of rice, costing Rs.18 per kg, will have value Rs.396
The total value of this 30 kg of rice = Rs.492 ......(a)
The mixture will weigh 30 kg and costs Rs.16.4 per kg
Total value of 30 kg of rice = Rs.492 ......(b)
Verified as (a) = (b) √